Boundary Value Problems

The fundamental solution to the Poisson equation with respect to a point-like excitation is known. Such a solution is called Green's function - in three dimensions, we have the famous \(1/r\)-dependency. However, if one knows the Green's function for a differential operator (here Laplace \(\Delta\)) any problem can be solved with respect to the given boundary conditions. In this section we will learn different techniques to solve such boundary value problems, for example the method of mirror charges or direct integrations.